Question

How many ounces of yogurt does the carton hold? (Hint: 1 ounce equals 1.805 in.³) round to the nearest tenth as needed

Answer 1

Answer:

The carton holds 8.9 ounces of yoghurt

Step-by-step explanation:

The upper diameter, D = 2 in

R = D/2

R = 2/2

The upper radius, R = 1 inch

`\begin{gathered} \text{The lower diameter, d= 2}(7)/(16)\text{ in = }2.4375 \\ \text{The lower radius, r = }(d)/(2)=\text{ }(2.4375)/(2)in\text{ = }1.22\text{ in} \end{gathered}`

The height, h = 3 in

The volume of the cone frustrum is:

`\begin{gathered} V=(1)/(3)\pi h(R^2+r^2+Rr) \\ V=(1)/(3)*3.142*3(1^2+1.22^2_{}+1.22(1)) \\ V=3.142(3.7084)) \\ V=11.65in^3 \end{gathered}`

1.805 in.³ = 1 ounce

11.65in.³ = 11.65/1.805 ounce

11.65in.³ = 6.5 ounces

The carton holds 6.5 ounces of yoghurt